ScalingStacks

Remark 4.4.2. The maps $\mu_{i,j}$ make $A=\bigoplus_{i\geq 0}E_{2}^{i}F_{1}^{i}$ into a monoid in the monoidal category of endofunctors of $\overline{{\mathcal{W}}}^{i}$, when $\overline{{\mathcal{W}}}^{i}$ has enough direct sums. If $\overline{{\mathcal{W}}}^{i}$ has enough colimits, we have an induced monoid $\bar{A}=\bigoplus_{i\geq 0}(E_{2}^{i}F_{1}^{i})\otimes_{H_{i}\otimes H_{i}^{\operatorname{opp}\nolimits}}H_{i}$. Now, the category $\Delta_{\lambda}{\mathcal{W}}$ is the category of $\bar{A}$-modules in $\overline{{\mathcal{W}}}^{i}$.